During fundraising, does the physical appearance of the solicitor impact the level of capital raised? An economist at the University of Nevada-Reno designed an experiment to answer this question and published the results in Economic Letters (Vol. 100.2008). Each in a sample of 955 households was contacted by a female solicitor and asked to contribute to the Center for Natural Hazards Mitigation Research. The level of contribution (in dollars) was recorded as well as the hair color of the solicitor (blond Caucasian, brunette Caucasian, or minority female).
a. Consider a model for the mean level of contribution, E(y), that allows for different means depending on the hair color of the solicitor. Create the appropriate number of dummy variables for hair color. (Use minority female as the base level.)
b. Write the equation of the model, part a, incorporating the dummy variables.
c. In terms of the β's in the model, what is the mean level of contribution for households contacted by a blond Caucasian solicitor?
d. In terms of the β's in the model, what is the difference between the mean level of contribution for households contacted by a blond solicitor and those contacted by a minority female?
e. One theory posits that blond solicitors will achieve the highest mean contribution level, but that there will be no difference between the mean contribution levels attained by brunette Caucasian and minority females. If this theory is true, give the expected signs of the β's in the model.
f. The researcher found the β-estimate for the dummy variable for blond Caucasian to be positive and significantly different from 0 (p-value < .01). The β-estimate for the dummy variable for brunette Caucasian was also positive, but not significantly different from 0 (p-value > .10). Do these results support the theory, part e?